Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received December 19, 2017; final manuscript received August 8, 2018; published online September 17, 2018. Assoc. Editor: Clement Gosselin.

Abstract

A new model for mechanical computing is demonstrated that requires only two basic parts, links, and rotary joints. These basic parts are combined into two main higher level structures, locks, and balances, and suffice to create all necessary combinatorial and sequential logic required for a Turing-complete computational system. While working systems have yet to be implemented using this new approach, the mechanical simplicity of the systems described may lend themselves better to, e.g., microfabrication, than previous mechanical computing designs. Additionally, simulations indicate that if molecular-scale implementations could be realized, they would be far more energy-efficient than conventional electronic computers.

Skakoon,
J. G.
, 2009, “
There's the Rub: Some Surprising Discoveries Are Made in the Quest of a Practically Frictionless Mechanical Operation,” Mechanical Engineering, American Society of Mechanical Engineers, New York.

A lock in the (0, 0) position (top), a lock in the (1, 0) position (bottom left), and a lock in the (0,1) position (bottom right). The (1,1) position is prohibited by the linkage geometry. See Fig. 16 for additional discussion.

A balance coupled to two locks. The inactive configuration is shown on the left. On the right, Lock0 Input has been activated, followed by activation of the balance input, which in turn activates Out put0.

Eight 1-bit full adders (wide blocks) are cascaded using ripple carry. As described in Sec. 4.2, multiple blocks can be cascaded using a four-phase clock. Narrow blocks are shift register cells, which form a delay line that stores portions of the results during computation. The final result appears on the outputs (right side) after two full clock cycles.

A two-cell shift register (left) shown with a plot of a four-phase clock cycle (right). In this example, the clock signal of cell 1 is driven by clock 1, and the clock signal of cell 2 is driven by clock 2.

A suitable multiphase clock signal can be generated mechanically using cams and followers. Here, a four-phase clock signal is generated using four identical cams spaced 90 deg out of phase. The four diagrams at the upper right show the cam at four rotations with only one of the four links. The collection of all four waveforms is shown in the right hand portion of Fig. 10.

A 4-cell shift register driven by a four-phase clock, shown at time t = 3/4. The last three cells are set to state 1 and the first cell in the blank state. Animations of this mechanism operating in forward and reverse are available in online.2,3 Solid models available online.4

A simple state machine. The main components are highlighted for comparison with Fig. 12. This state machine implements the transition table shown in Fig. 14. A table of the schematic symbols used in this drawing is provided in the Appendix (Fig. 26).

Analyzing lock holding force. In the ideal case (upper left), the lock has two overlapping sets of solutions: θ0=0,θ1≠0 and θ0≠0,θ1=0, with a kinematic branch point [25,26] at θ0=0,θ1=0. Link flexibility can be modeled by replacing one of the links with a spring (lower left). The contour plot shows level sets of spring energy as a function of input angles. In the ideal case, an arbitrarily large force can be locked without affecting the other input. In the more realistic case including link flexibility, a small holding force on one input can hold a large force on the other input.

A flexure-based implementation of the system shown in Fig. 22, made of two or three stacked layers (a second outer layer can be added to make a three-layer assembly for increased rigidity). Interlayer bonds are shown as dark dots in the lower right image. Solid models available online.4

Part of a molecular mechanical logic gate. This molecular machine consists of 120,695 atoms, 87,595 carbon and 33,100 hydrogen, and occupies a volume of about 27 nm × 32 nm × 7 nm. The nine rigid links are connected to each other via a pair of rotary joints. Atomic structure file available online.4

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